Jean-Claude Juncker, the president-elect of the next European Commission, has received “at least two names” of possible candidates from Denmark, according to Danish media.

The names of the Danish nominees have not yet been made public, but speculation about who will be Connie Hedegaard's successor is rife.

Danish newspaper Berlingske reported that prime minister Helle Thorning-Schmidt may have nominated Christine Antorini, the education minister, and Morten Bødskov, the former justice minister, both of whom are centre-left politicians.

Earlier reports suggested that Karen Angelo Hækkerup, the justice minister, and Mette Gjerskov, the leader of the Social Democrats group in the Danish parliament, were also being considered, as well as Margrethe Vestager, the economic and interior affairs minister – the only candidate from the liberals.

Juncker was keen to receive several names from each country so he would have more choice when composing his ideal cabinet. It is believed that Thorning-Schmidt has spoken with Juncker several times over the past couple of weeks. Her strategy of not making the names of the candidates public may increase the chances of her commissioner getting one of the senior portfolios.

Denmark is one of only five countries that have not officially announced their European Commission candidate. The Netherlands, Cyprus, Slovenia and Belgium are also yet to be confirmed. The decisions are expected to be finalised at the European Council meeting on 30 August.

Thorning-Schmidt is among the names of possible successors to Herman Van Rompuy as president of the European Council.